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Abstract

We demonstrate that trapping of dispersive waves between two optical solitons takes place when resonant scattering of the waves on the solitons leads to nearly perfect reflections. The momentum transfer from the radiation to solitons results in their mutual attraction and a subsequent collision. The spectrum of the trapped radiation can either expand or shrink in the course of the propagation, which is controlled by arranging either collision or separation of the solitons.

Figures (5)

(a) The dispersion diagram and resonances between the reflected and incident waves predicted by roots of Eq. (4), with δ = 0 corresponding to the soliton frequency. (b,c) The single event of the scattering of a dispersive pulse on the soliton for the incident pulse with frequency δr (b) and δi (c), respectively. Here, β3 = −0.015, the soliton input is
A=2qsech(2q(t−ts)), q = 18, ts = 10. The input for the dispersive pulse is
A=Isech((t−t0)8/w8)eiδr,it, with t0 = 12, and
I=0.4w = 5 in (b) and
I=0.5, w = 12 in (c).

(a) The soliton collision caused by the effective attraction due to multiple scattering of dispersive waves. Initial solitons have zero frequencies and q = 12.5, the dispersive pulse is
A=Isech(t/w)eiδt,
I=0.25, δ = −28. (b) The change of the dispersive-pulse’s spectrum following the collision shown in (a). (c) The collision distance (zc) vs. the initial amplitude of the dispersive pulse (
I). For comparison, the best fit to dependence
zc~1/I (see the text) is shown in (c) too.

The narrowing of the radiation spectrum trapped between two separating solitons. The initial solitons are taken with q = 12.5 and frequencies δ = 1.5, δ = 0. (a) The dispersion diagram showing the scattering cascade. (b,c) The evolution in the temporal and frequency domains. In this case, β3 = −0.01.